Method and apparatus for estimating SOC of a battery

ABSTRACT

A method of determining a state-of-charge for a battery is provided. A startup state-of-charge of the battery is determined as a function of a present open circuit voltage measurement for a present ignition startup, at least one open circuit voltage observation of a previous ignition startup, and a current draw integration over a time period from a previous ignition startup event to a present ignition startup event. A run state-of-charge change of the battery is determined for an ignition key-on operation. The run state-of-charge change comprises a difference between the present open circuit voltage measurement and the at least one previous open circuit voltage observation, and is determined in response to of a current draw integration over a respective period of time. The state-of-charge of the battery is calculated based on a function of the startup state-of-charge and the run state-of-charge change of the battery.

BACKGROUND OF INVENTION

An embodiment relates generally to determining a state of charge of abattery within a vehicle.

Determining a state-of-charge (SOC) for a battery can be performedutilizing various techniques utilizing coulomb counting or parameterestimations techniques. Coulomb counting involves the use of onemeasurement (i.e., one open circuit voltage reading) to estimate thebattery state-of-charge. The accuracy of the open circuit voltage iscritical to determining a state of charge. If there is measurementerror, then the state-of-charge estimation will be in error by basicallythe factor of the measurement error.

Moreover, coulomb counting utilizing charge efficiency and batterycapacity to determine state-of-charge often use the standardmanufacturing specification values for a new battery values throughoutthe estimation process for the life of the battery. Over time thebattery ages and charge efficiency and battery capacity changes as wellthereby creating error in the state-of-charge estimation.

Current parameter estimation techniques require excitations which arenot necessarily available on conventional vehicles.

SUMMARY OF INVENTION

An advantage of an embodiment is the determination of a state of chargeof a battery where error in estimating the state of charge is reduced byutilizing the integration of both present and previous open circuitvoltage measurements/estimations and current draws. Deficiencies ofprior art techniques are overcome by not solely basing the determinationof the battery capacity on a new battery. Since battery characteristicschange over a life of the battery, utilizing both present and pastbattery characteristic measurements/estimations provide a morecomprehensive analysis as to how the battery is changing over a courseof time which reduces any anomalies that may occur in a singlemeasurement/estimation.

An embodiment contemplates a method of determining a state-of-charge fora battery. Open circuit voltages of a vehicle battery are measuredduring ignition startups. A startup state-of-charge of the battery isdetermined as a function of a present open circuit voltage measurementfor a present ignition startup, at least one open circuit voltageobservation of a previous ignition startup, and a current drawintegration over a time period from a previous ignition startup event toa present ignition startup event. A run state-of-charge change of thebattery is determined for an ignition key-on operation. The runstate-of-charge change comprises a difference between the present opencircuit voltage measurement and the at least one previous open circuitvoltage observation, and is determined in response to of a current drawintegration over a respective period of time. The state-of-charge of thebattery is calculated based on a function of the startup state-of-chargeand the run state-of-charge change of the battery.

An embodiment contemplates a system for determining a state-of-charge ofa battery. The system includes a battery, at least one component fordrawing power from the battery, a voltmeter for measuring an opencircuit voltage of the battery at ignition start sequences, a currentsensor for sensing current drawn from the battery. The system furtherincludes a control module for determining a state-of-charge of a batteryas a function of the startup state-of-charge and the run state-of-chargechange of the battery. The startup state-of-charge is determined at atime of an ignition startup event. The startup state-of-charge isfurther a function of a present open circuit voltage measurement for apresent ignition startup, at least one previous open circuit voltageobservation, and a current integration over time period from a previousignition event to a present ignition event. The run state-of-chargechange comprises at a time during an ignition on operation. The runstate-of-charge change being estimated as a difference between thepresent open circuit voltage measurement and at least one previous opencircuit voltage observation determined in response to currentintegration over a respective period of time*

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a block diagram system for estimating a state-of-charge (SOC)and battery capacity of a battery.

FIG. 2 is a timeline schematic illustrating time instances fordetermining open circuit voltages.

FIG. 3 a flowchart of a method for determining a state of charge (SOC)of a battery and battery capacity.

DETAILED DESCRIPTION

FIG. 1 illustrates a block diagram of an embodiment of a vehicle 10incorporating a state-of-charge (SOC) and battery capacity estimationsystem. It should be understood that the vehicle may include, but is notlimited to, hybrid vehicles, internal combustion vehicles, and electricvehicles or any machinery that utilizes batteries. The vehicle 10includes a battery pack 12 having a single battery or a plurality ofindividual battery modules. For example, an embodiment may include aplurality of batteries connected in series to produce a high voltagenominal voltage or a vehicle may include a single 12 volt batteryproducing a 14 volt nominal voltage for an internal combustion vehicle.The state-of-charge and battery capacity estimation technique describedherein may be applicable to variety of battery types, including but notlimited to, nickel metal hydride (NiMH) batteries, lead acid batteries,or lithium ion batteries.

The vehicle battery 12 is electrically coupled to a plurality of devices14 which utilize the battery as a power source. The vehicle 10 mayfurther include a current sensor 16, and voltage meter 18, and a controlmodule 20.

The plurality of devices 14 include, but are not limited to, poweroutlets adapted to an external plug in device, accessories, components,subsystems, and systems of a vehicle. The current sensor 16 is used tomonitor the current leaving the vehicle battery 12. The voltmeter 18measures a voltage so that an open circuit voltage may be determined. Acontrol module 20, or similar module, obtains, derives, monitors, and/orprocesses a set of parameters associated with vehicle battery 12. Theseparameters may include, without limitation, current, voltage,state-of-charge (SOC), battery capacity, battery internal resistances,battery internal reactance, battery temperature, and power output of thevehicle battery. The control module 20 includes an algorithm, or like,for executing a vehicle state-of-charge and battery capacity estimationtechnique. In a hybrid vehicle or electric vehicle, it is typical that acurrent sensor is integral to the control module.

To enhance battery charging control and vehicle power management, theopen circuit voltage V_(oc) is used to estimate the SOC. The SOC of thebattery is estimated utilizing a startup SOC and a run SOC change. Theformula for the SOC of the battery is represented as follows:S _(oc)=SOC_(startup)+SOC_(running) =f(V _(oc)(0),T)+θ∫Idt  (1)where f(V_(oc)(0),T) is the startup SOC that is a function of the opencircuit voltage and temperature, and θ∫Idt is the run SOC change that isa function of a battery parameter θ and previous current dataintegration. The battery parameter

$\theta\left( {= \frac{c}{Q}} \right)$is a function of battery charge efficiency c and battery capacity Q.

The open circuit voltage V_(oc) is a key element in determining the SOC.Therefore the following embodiment will focus on how V_(oc) is derivedand utilized in determining SOC_(startup) and SOC_(running).

FIG. 2 illustrates a timeline for estimating a plurality of open circuitvoltages for SOC_(startup) which takes into consideration historicaldata. Historical data relates to previous instances of time at which anignition off and ignition on event is detected and batterycharacteristics are observed. The term observed used herein refers tomeasured and/or estimated values based on measurements. A timingsequence of continuous ignition on I_(n) and ignition off I_(f) eventsis shown generally at 20. Timeline 22 illustrates each of the timeinstances when the ignition transitions from an ignition-off to anignition-on (e.g., t_(k-2),t_(k-1),t_(k)). Based on the different timeinstances, an open circuit voltage may be determined for each timeinstance taking into consideration not only the present open circuitvoltage measurement, but also previous open circuit voltage measurementsfor estimating a more precise open circuit voltage value at the k_(th)ignition event. Formulas for the time instances t_(k-2),t_(k-1),t_(k)shown in FIG. 2 are represented by the following formulas:

$\begin{matrix}{{{\hat{V}}_{oc}\left( {t_{k},t_{k}} \right)} = {V_{oc}\left( t_{k} \right)}} & (2) \\{{{\hat{V}}_{oc}\left( {t_{k},t_{k - 1}} \right)} = {{V_{oc}\left( t_{k - 1} \right)} + {\theta{\int_{t_{k - 1}}^{t_{k}}{I{\mathbb{d}t}}}}}} & (3) \\{{{\hat{V}}_{oc}\left( {t_{k},t_{k - 2}} \right)} = {{V_{oc}\left( t_{k - 2} \right)} + {\theta{\int_{t_{k - 1}}^{t_{k}}{I{\mathbb{d}t}}}} + {\theta{\int_{t_{k - 2}}^{t_{k - 1}}{I{\mathbb{d}t}}}}}} & (4)\end{matrix}$

When taking into consideration the past observations, a weighted averageis obtained utilizing an adjustment factor λ. The adjustment factor λweights the open circuit voltage estimation based on the duration of thekey-off time or the key-on time. It should be understood that thetechnique described herein for determining the adjustment factor is onlyone embodiment of how the adjustment factor may be determined and thatother techniques used to determine the adjustment factor may be appliedherein without deviating from the scope of the invention. The formulafor determining the open circuit voltage utilizing the adjustment factoris represented by the following formula:

$\begin{matrix}{{{\hat{V}}_{oc}\left( t_{k} \right)} = {{\lambda\left\{ {{\hat{V}\left( t_{k - 1} \right)} + {\hat{\theta}{\int_{t_{k - 1}}^{t_{k}}{{\mathbb{i}}{\mathbb{d}t}}}}} \right\}} + {\left( {1 - \lambda} \right){{V_{oc}\left( t_{k} \right)}.{where}}\mspace{14mu}\left\{ {{\hat{V}\left( t_{k - 1} \right)} + {\hat{\theta}{\int_{t_{k - 1}}^{t_{k}}{{\mathbb{i}}{\mathbb{d}t}}}}} \right\}}}} & (5)\end{matrix}$represents the estimation based on previous observation (t_(k-n)), and(1−λ)V_(oc)(t_(k)) represents a present observation (t_(k)).

Therefore, if the key-off time is too short, then a greater emphasis isplaced on the estimated value in which the adjustment factor would bepreferably close to 1. If the key-off time is greater than apredetermined time value, then a greater emphasis is placed on thecurrent observation, and the adjustment factor would be preferably closeto 0. As a result, the following formula is used to determine theadjustment factor λ which is a function of the time off. The adjustmentfactor λ for the open circuit voltage is represented by the followingformula:λ=e ^(−t) ^(off) ^((t) ^(k) ^()/τ)  (6)where t_(off) is a time from when the ignition key is turned off to atime the ignition is turned on, t_(k) is a time the ignition key isturned on at the k_(th) ignition interval, and τ is a time constant.

The battery parameter θ is commonly determined by a ratio of the chargeefficiency and the battery capacity. Charge efficiency and batterycapacity values are typically nominal values based on a new battery.However, such parameters change as the battery ages, and as a result,are not robust factors for determining the battery parameter θ. Sincethese parameters change with age, the battery parameter θ should beestimated periodically. To estimate the battery parameter θ on aperiodic basis (e.g., at least once a month), the battery parameter θ issolved for utilizing the open circuit voltage formula which isrepresented as follows:

$\begin{matrix}{{{\hat{V}}_{oc}\left( t_{k} \right)} = {{{\hat{V}}_{oc}\left( t_{k - 1} \right)} + {{\hat{\theta}}_{k}{\int_{t_{k - 1}}^{t_{k}}{I{{\mathbb{d}t}.}}}}}} & (7)\end{matrix}$By modifying the open circuit voltage {circumflex over (V)}_(oc)(t_(k))to solve for θ, the resulting battery parameter θ is represented asfollows:

$\begin{matrix}{{\hat{\theta}}_{k} = \frac{{V_{oc}\left( t_{k} \right)} - {{\hat{V}}_{oc}\left( t_{k - 1} \right)}}{\int_{t_{k - 1}}^{t_{k}}{I{\mathbb{d}t}}}} & (8)\end{matrix}$To compensate for short ignition key-off times, an adjustment factor isincorporated in the battery parameter estimation formula. The adjustmentfactor for the battery parameter λ_(θ) is represented by the followingformula:λ_(θ) =e ^(−t) ^(off) ^((t) ^(k) ^()/τ) ^(θ)   (9)The resulting formula for the battery parameter is as follows:

$\begin{matrix}{{\hat{\theta}}_{k} = {{\lambda_{\theta}{\hat{\theta}}_{k - 1}} + {\left( {1 - \lambda_{\theta}} \right)\frac{{V_{oc}\left( t_{k} \right)} - {{\hat{V}}_{oc}\left( t_{k - 1} \right)}}{\int_{t_{k - 1}}^{t_{k}}{I{\mathbb{d}t}}}}}} & (10)\end{matrix}$where θ_(k-1) is the previous battery parameter estimation and

$\frac{{V_{oc}\left( t_{k} \right)} - {{\hat{V}}_{oc}\left( t_{k - 1} \right)}}{\int_{t_{k - 1}}^{t_{k}}{I{\mathbb{d}t}}}$a present battery parameter estimation.

Due to temperature differences when measurements for current andprevious open circuit voltage are obtained, the estimation techniquegenerated herein requires normalization between the open circuit voltagemeasurements. That is, each open circuit voltage (i.e., both present andprevious), must be normalized at a standard temperature so that presentobservations and past observations can be cooperatively utilized. As aresult, each open circuit voltage for a respective ignition event isconverted to an open circuit voltage based on a normalized temperature.The conversion may be performed utilizing an algorithm, lookup table, orthe like. For example, a normalized formula utilizing a standardizedtemperature, such as 25 degrees, is represented as follows:

$\begin{matrix}{{{\hat{V}}_{oc}^{25}\left( t_{k} \right)} = {{\lambda\left\{ {{{\hat{V}}_{oc}^{25}\left( t_{k - 1} \right)} + {{\hat{\theta}}_{k - 1}^{25}{\int_{t_{k - 1}}^{t_{k}}{{\mathbb{i}}{\mathbb{d}t}}}}} \right\}} + {\left( {1 - \lambda} \right){{V_{oc}^{25}\left( t_{k} \right)}.}}}} & (11)\end{matrix}$The battery parameter using normalized temperatures is as follows:

$\begin{matrix}{{\hat{\theta}}_{k}^{25} = {{\lambda_{\theta}{\hat{\theta}}_{k - 1}^{25}} + {\left( {1 - \lambda_{\theta}} \right){\frac{{V_{oc}^{25}\left( t_{k} \right)} - {{\hat{V}}_{oc}^{25}\left( t_{k - 1} \right)}}{\int_{t_{k - 1}}^{t_{k}}{I{\mathbb{d}t}}}.}}}} & (12)\end{matrix}$As a result, the open circuit voltage for the SOC of the vehicle batterycan be represented by the following formula:{circumflex over (V)} _(oc) ²⁵(t,t _(k))={circumflex over (V)} _(oc)²⁵(t _(k))+θ_(k) ²⁵∫_(t) _(k) ^(t) Idt.  (13)

Once the normalized open circuit voltage {circumflex over (V)}_(oc) ²⁵(t, t_(k)) for the SOC of the battery is determined, the normalized opencircuit voltage is converted back to the open circuit voltage at thecurrent temperature and is represented by {circumflex over (V)}_(oc)(t).

The SOC charge of the battery is determined utilizing {circumflex over(V)}_(oc)(t) that incorporates estimations of both current measurementsand previous measurements. The other factors in determining SOC can bebasically grouped as a linear mapping constant. As a result, the SOC ofthe vehicle battery at the present instance of time may be representedby the following formula:SOC(t)=f({circumflex over (V)} _(oc)(t),T)  (14)where {circumflex over (V)}_(oc)(t) is the estimated open circuitvoltage of the battery using current measurements and previousmeasurements, and T is a respective temperature at the time of themeasurement.

The battery capacity Q is also determined utilizing current measurementsand battery parameters. The battery capacity is derived utilizing thefollowing formula represented by:Q _(actual) ²⁵ =Q _(new) ²⁵(θ_(new) ²⁵/θ_(k) ²⁵)  (15)where Q_(actual) ²⁵ is the normalized estimated battery capacity of thebattery, Q_(new) ²⁵ is a normalized battery capacity of a new battery,θ_(new) ²⁵ is a normalized battery parameter of a new battery, and{circumflex over (θ)}_(k) ²⁵ is the normalized estimated batteryparameter as a function of an adjustment factor. It should be understoodthat in deriving the battery capacity, estimations must be derived usinga standard temperature (e.g., 25 degrees). The formula for determiningthe battery parameter at the k_(th) ignition start is represented by thefollowing formula:

$\begin{matrix}{{\hat{\theta}}_{k}^{25} = {{\lambda_{\theta}{\hat{\theta}}_{k - 1}^{25}} + {\left( {1 - \lambda_{\theta}} \right)\frac{{V_{oc}^{25}\left( t_{k} \right)} - {{\hat{V}}_{oc}^{25}\left( t_{k - 1} \right)}}{\int_{t_{k - 1}}^{t_{k}}{I{\mathbb{d}t}}}}}} & (16)\end{matrix}$

FIG. 3 illustrates a flowchart for a technique for estimating the SOCand battery capacity utilizing V_(oc) data. In step 30, a first key-onevent is initiated. The first key-on represents a time when the vehicleignition is first started and data is collected. The first key-on eventmay also represent a time when the vehicle ignition is started directlyafter the vehicle battery is replaced and data is obtained for the newbattery. In this manner, previous data relating to past batteryoperating conditions and parameters would no longer be valid since thenew battery would have different charging and efficiency characteristics(e.g., charge efficiency values and battery capacity values).

In step 31, the measurable parameters and estimated parameters areinitialized. That is, at the initiation of a new vehicle startup or whenthe battery is replaced, all variables for the each of the formulasdescribed above are re-set to their initial conditions. For example,k=0, λ=0, λ_(θ)=1, θ₀ ²⁵=θ_(new) ²⁵ , {circumflex over (V)} _(oc)²⁵(0)=13V, ΔQ=Q _(new) ²⁵.

In step 32, the present open circuit voltage V_(oc)(t_(k)) and thebattery temperature T are measured.

In step 33, the open circuit voltage V_(oc)(t_(k)) is converted to anopen circuit voltage at a standard temperature V_(oc) ²⁵(t_(k)). Theconversion may be performed using an algorithm or a lookup table.

In step 34, the startup voltage is updated using the formula set forthin equation (11).

In step 35, the battery parameter is updated using the formula set forthin equation (12).

In step 36, the battery capacity is updated using the formula set forthin equation (15).

In step 37, the current integration ∫Idt is reset to zero.

In step 38, a determination is made whether the ignition key is in thekey-off position. If the ignition is in the key-off position, then theroutine proceeds to step 39; otherwise the routine proceeds to step 47.

In step 39, the key-off time is reset to zero (t_(off)=0). Thisinitiates a counter for determining how long the ignition is in thekey-off position.

In step 40, a determination is made whether the ignition key is in thekey-on position. If the ignition key is not in the key-on position, thenthe routine proceeds to step 41.

In step 41, the routine waits for a period of time before updating thekey-off time.

In step 42, the key-off time is updated. The key-off time is representedby the following formula:t _(off) =t _(off) +Δt _(off)where t_(off) is a summation of the key-off time since the resetting thekey-off time, and Δt_(off) is the additive time period elapsed in step41.

In step 43, the current measurement (I) of the battery is measured.

In step 44, the current integration is updated which incorporates thepresent current measurement with the past current measurements. Theroutine proceeds back to step 40.

In step 40, if the determination is made that the ignition key is on,then the routine proceeds to step 45, otherwise, the routine proceeds tostep 41.

In step 45, a key-on cycle count is updated. The key-on cycle count isthe number of times the ignition key has been turned on since systeminitialization in step 31. Each time the ignition key is turned on, thecount is increased by 1.

In step 46, the adjustment factor is determined for the open circuitvoltage as set forth in equation (6) and the adjustment factor isdetermined for the battery parameter as set forth in equation (8).Thereafter, a return is made to step 32 to execute steps 32-38 asdescribed above.

In step 38, if the determination is made that the ignition key is not inthe key-off position, then the routine proceeds to step 47.

In step 47, the current (I) leaving the battery and the temperature (T)is measured.

In step 48, the current integration is updated based on the past topresent measurements.

In step 49, the running open circuit voltage {circumflex over (V)}_(oc)²⁵(t) at the standard temperature is updated using the formula set forthin equation (13).

In step 50, the running open circuit voltage {circumflex over (V)}_(oc)²⁵(t) is converted back to a running open circuit voltage {circumflexover (V)}_(oc)(t) at the present temperature using an algorithm or alookup table.

In step 51, the SOC for the battery at the present temperature isdetermined using the formula set forth in equation (14).

In step 52, a predetermined period of time elapses before returning tostep 38.

The battery capacity derived in step 36 and the SOC derived step 51 areeither displayed to the driver of the vehicle identifying the conditionof the battery or may be represented in some other capacity forindicating the SOC and battery capacity.

While certain embodiments of the present invention have been describedin detail, those familiar with the art to which this invention relateswill recognize various alternative designs and embodiments forpracticing the invention as defined by the following claims.

What is claimed is:
 1. A method of determining a state-of-charge for abattery, the method comprising the steps of: measuring open circuitvoltages of a vehicle battery during ignition startups by a voltmeter;determining a startup state-of-charge of the battery by a control moduleas a function of a present open circuit voltage measurement for apresent ignition startup, at least one open circuit voltage observationof a previous ignition startup, and a current draw integration over atime period from a previous ignition startup event to a present ignitionstartup event; determining a run state-of-charge change of the batteryby the control module for an ignition key-on operation, the runstate-of-charge change comprising a difference between the present opencircuit voltage measurement and the at least one previous open circuitvoltage observation, and determined in response to a current drawintegration over a respective period of time; and calculating thestate-of-charge of the battery by the control module based on a functionof the startup state-of-charge and the run state-of-charge change of thebattery.
 2. The method of claim 1 wherein the state-of-charge for abattery is represented by the following formula:S _(oc)=SOC_(startup)+SOC_(running) =f(V _(oc)(0),T)+θ∫Idt wheref(V_(oc)(0),T) is the startup state-of-charge and is a function of theopen circuit voltage and temperature, and θ∫Idt is a run state-of-chargechange and is a function of a battery parameter and the current drawintegration over the respective period of time.
 3. The method of claim 2wherein the startup state-of-charge is derived from an open circuitvoltage estimation based on the following formula:V̂_(oc)(t_(k)) = λ{V̂(t_(k − 1)) + θ̂∫_(t_(k − 1))^(t_(k))i𝕕t} + (1 − λ)V_(oc)(t_(k))where V_(oc)(t) is the present open circuit voltage measurement at thek_(th) ignition start, {circumflex over (V)}_(oc)(t_(k−1)) is theprevious open circuit voltage observation, {circumflex over (θ)} is thebattery parameter, I is a current draw from the battery, and λ is anadjustment factor.
 4. The method of claim 3 wherein the adjustmentfactor is represented by the following formula:λ=e ^(−t) ^(off) ^((t) ^(k) ^()/τ) where t_(off) is an elapsed timebetween an ignition key-on operation and an ignition key-off operation,t_(k) is a time the ignition key is turned on at the k_(th) ignitioninterval, and τ is a time constant.
 5. The method of claim 3 wherein thebattery parameter θ is a function of a previous battery parameterobservation and a present estimated battery parameter.
 6. The method ofclaim 5 wherein the battery parameter θ is represented by the followingformula:${\hat{\theta}}_{k} = {{\lambda_{\theta}{\hat{\theta}}_{k - 1}} + {\left( {1 - \lambda_{\theta}} \right)\frac{{V_{oc}\left( t_{k} \right)} - {{\hat{V}}_{oc}\left( t_{k - 1} \right)}}{\int_{t_{k - 1}}^{t_{k}}{I{\mathbb{d}t}}}}}$where λ_(θ) is an adjustment factor for the battery parameter,λ_(θ){circumflex over (θ)}_(k-1) is a previous battery parameterobservation, and$\frac{{V_{oc}\left( t_{k} \right)} - {{\hat{V}}_{oc}\left( t_{k - 1} \right)}}{\int_{t_{k - 1}}^{t_{k}}{I{\mathbb{d}t}}}$is a present battery parameter observation.
 7. The method of claim 6wherein the adjustment factor for the battery parameter is a function ofa time that an ignition key is off, and wherein the adjustment factor isdetermined by the following formula:λ=e ^(−t) ^(off) ^((t) ^(k) ^()/τ) _(θ).
 8. The method of claim 6wherein the present open circuit voltage measurement, the previous opencircuit voltage observation, and the battery parameter are normalized ata respective temperature.
 9. The method of claim 8 wherein the opencircuit voltages for the startup state-of-charge and the runstate-of-charge change are normalized at a respective temperature. 10.The method of claim 9 wherein a normalized open circuit voltage for thestate-of-charge of the battery is determined as a function of the opencircuit voltage determined for the startup state-of-charge at therespective temperature, and a function of the battery parameter andcurrent integration for the run state-of-charge change at the respectivetemperature.
 11. The method of claim 10 wherein the normalized opencircuit voltage for the state-of-charge of the battery is converted backto an open circuit voltage at a current temperature.
 12. The method ofclaim 11 wherein the state-of-charge of the battery is determined as afunction of the open circuit voltage at the current temperature.
 13. Themethod of claim 1 wherein the state of charge of the battery isdisplayed to user of the vehicle via a display device.
 14. The method ofclaim 1 wherein a representation of the state of charge of the batteryis displayed to user of the vehicle via a display device.
 15. A systemfor determining a state-of-charge of a battery comprising: a battery; atleast one component for drawing power from the battery; a voltmeter formeasuring an open circuit voltage of the battery at ignition startsequences; a current sensor for sensing current drawn from the battery;and a control module for determining a state-of-charge of a battery as afunction of the startup state-of-charge and the run state-of-chargechange of the battery, the startup state-of-charge being determined at atime of an ignition startup event, the startup state-of-charge being afunction of a present open circuit voltage measurement for a presentignition startup, at least one previous open circuit voltageobservation, and a current integration over time period from a previousignition event to a present ignition event, the run state-of-chargechange comprising at a time during an ignition on operation, the runstate-of-charge change being estimated as a difference between thepresent open circuit voltage measurement and at least one previous opencircuit voltage observation determined in response to currentintegration over a respective period of time.
 16. The system of claim 15wherein the control module determines the startup state-of-charge froman estimated open circuit voltage based on the following formula:V̂_(oc)(t_(k)) = λ{V̂(t_(k − 1)) + θ̂∫_(t_(k − 1))^(t_(k))i𝕕t} + (1 − λ)V_(oc)(t_(k))where V_(oc)(t) is the present open circuit voltage measurement at thek_(th) ignition start, {circumflex over (V)}_(oc)(t_(k-1)) is theprevious open circuit voltage observation, {circumflex over (θ)} is abattery parameter, I is a current draw from the battery, and λ is anadjustment factor.
 17. The system of claim 16 wherein the control moduledetermines the adjustment factor based on the following formula:λ=e ^(−t) ^(off) ^((t) ^(k) ^()/τ) where t_(off) is an elapsed timebetween an ignition key-on operation and an ignition key-off operation,t_(k) is a time the ignition key is turned on at the k_(th) ignitioninterval, and τ is a time constant.
 18. The system of claim 17 whereinthe control module determines the battery parameter based on thefollowing formula:${\hat{\theta}}_{k} = {{\lambda_{\theta}{\hat{\theta}}_{k - 1}} + {\left( {1 - \lambda_{\theta}} \right)\frac{{V_{oc}\left( t_{k} \right)} - {{\hat{V}}_{oc}\left( t_{k - 1} \right)}}{\int_{t_{k - 1}}^{t_{k}}{I{\mathbb{d}t}}}}}$where λ_(θ) is an adjustment factor for the battery parameter,λ_(θ){circumflex over (θ)}_(k-1) is a previous battery parameterobservation, and$\frac{{V_{oc}\left( t_{k} \right)} - {{\hat{V}}_{oc}\left( t_{k - 1} \right)}}{\int_{t_{k - 1}}^{t_{k}}{I{\mathbb{d}t}}}$is a present battery parameter observation.
 19. The system of claim 15wherein the control module determines the adjustment factor for thebattery parameter based on the following formula:λ=e ^(−t) ^(off) ^((t) ^(k) ^()/τ) ^(θ) .
 20. The system of claim 15further comprising a display for identifying the state of charge of thebattery to a user of the vehicle.